Question

According to the Bohr Theory, which of the following transitions in the hydrogen atom will give rise to the least energetic photon ?
a) n = 6 to n = 1
b) n = 5 to n = 4
c) n = 5 to n = 3
d) n = 6 to n = 5

Answer 1

According to Bohr's theory ,
$\bold{\Delta{E}\propto\left[\begin{array}{c}{1/n_1^2-1/n_2^2}\end{array}\right]}$
now, Let's check all options
(a) n = 6 to n = 1
[1/1² - 1/6²] = [1 - 1/36] = 35/36

(b) n = 5 to n = 4
[1/4² - 1/5²] = 1/16 - 1/25 = 9/400

(c) n = 5 to n = 3
[1/3² - 1/5²] = 1/9 - 1/25 = 16/225

(d) n = 6 to n = 5
[1/5² - 1/6²] = 1/25 - 1/36 = 11/900

Here least value of [1/n₁² - 1/n₂²] for option (d)
Hence, answer is option (d) n = 6 to n = 5

Answer 2

The answer is option (d).